The proximity effect from a spin-triplet $p_x$-wave superconductor to a dirty normal-metal has been shown to result in various unusual electromagnetic properties, reflecting a cooperative relation between topologically protected zero-energy quasipart
icles and odd-frequency Cooper pairs. However, because of a lack of candidate materials for spin-triplet $p_x$-wave superconductors, observing this effect has been difficult. In this paper, we demonstrate that the anomalous proximity effect, which is essentially equivalent to that of a spin-triplet $p_x$-wave superconductor, can occur in a semiconductor/high-$T_c$ cuprate superconductor hybrid device in which two potentials coexist: a spin-singlet $d$-wave pair potential and a spin--orbit coupling potential sustaining the persistent spin-helix state. As a result, we propose an alternative and promising route to observe the anomalous proximity effect related to the profound nature of topologically protected quasiparticles and odd-frequency Cooper pairs.
Lattice deformations act on the low-energy excitations of Dirac materials as effective axial vector fields. This allows to directly detect quantum anomalies of Dirac materials via the response to axial gauge fields. We investigate the parity anomaly
in Dirac nodal line semimetals induced by lattice vibrations, and establish a topological piezoelectric effect; i.e., periodic lattice deformations generate topological Hall currents that are transverse to the deformation field. The currents induced by this piezoelectric effect are dissipationless and their magnitude is completely determined by the length of the nodal ring, leading to a semi-quantized transport coefficient. Our theoretical proposal can be experimentally realized in various nodal line semimetals, such as CaAgP and Ca$_{_3}$P${_2}$.
Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts
a time-reversal-symmetry protected $mathbb{Z}_2$ topological quantum paramagnet ({em topological triplon insulator}) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial $mathbb{Z}_2$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the $mathbb{Z}_2$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the $mathbb{Z}_2$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d$^{4}$ Mott insulators, and their potential applications.
It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily b
e manipulated by an applied field. Here we study triplon excitations in an S=1/2 quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By the bulk-boundary correspondence, we find that the non-zero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.
We classify interacting topological insulators and superconductors with order-two crystal symmetries (reflection and twofold rotation), focusing on the case where interactions reduce the noninteracting classification. We find that the free-fermion $m
athbb{Z}_2$ classifications are stable against quartic contact interactions, whereas the $mathbb{Z}$ classifications reduce to $mathbb{Z}_N$, where $N$ depends on the symmetry class and the dimension $d$. These results are derived using a quantum nonlinear $sigma$ model (QNLSM) that describes the effects of the quartic interactions on the boundary modes of the crystalline topological phases. We use Clifford algebra extensions to derive the target spaces of these QNLSMs in a unified way. The reduction pattern of the free-fermion classification then follows from the presence or absence of topological terms in the QNLSMs, which is determined by the homotopy group of the target spaces. We show that this derivation can be performed using either a complex fermion or a real Majorana representation of the crystalline topological phases and demonstrate that these two representations give consistent results. To illustrate the breakdown of the noninteracting classification we present examples of crystalline topological insulators and superconductors in dimensions one, two, and three, whose surfaces modes are unstable against interactions. For the three-dimensional example, we show that the reduction pattern obtained by the QNLSM method agrees with the one inferred from the stability analysis of the boundary modes using bosonization.
We show that for two-band systems nonsymmorphic symmetries may enforce the existence of band crossings in the bulk, which realize Fermi surfaces of reduced dimensionality. We find that these unavoidable crossings originate from the momentum dependenc
e of the nonsymmorphic symmetry, which puts strong restrictions on the global structure of the band configurations. Three different types of nonsymmorphic symmetries are considered: (i) a unitary nonsymmorphic symmetry, (ii) a nonsymmorphic magnetic symmetry, and (iii) a nonsymmorphic symmetry combined with inversion. For nonsymmorphic symmetries of the latter two types, the band crossings are located at high-symmetry points of the Brillouin zone, with their exact positions being determined by the algebra of the symmetry operators. To characterize these band degeneracies we introduce a emph{global} topological charge and show that it is of $mathbb{Z}_2$ type, which is in contrast to the emph{local} topological charge of Fermi points in, say, Weyl semimetals. To illustrate these concepts, we discuss the $pi$-flux state as well as the SSH model at its critical point and show that these two models fit nicely into our general framework of nonsymmorphic two-band systems.
As PT and CP symmetries are fundamental in physics, we establish a unified topological theory of PT and CP invariant metals and nodal superconductors, based on the mathematically rigorous $KO$ theory. Representative models are constructed for all non
trivial topological cases in dimensions $d=1,2$, and $3$, with their exotic physical meanings being elucidated in detail. Intriguingly, it is found that the topological charges of Fermi surfaces in the bulk determine an exotic direction-dependent distribution of topological subgap modes on the boundaries. Furthermore, by constructing an exact bulk-boundary correspondence, we show that the topological Fermi points of the PT and CP invariant classes can appear as gapless modes on the boundary of topological insulators with a certain type of anisotropic crystalline symmetry.
Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore,
even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of d_{xy}-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge states. The leading instabilities are Majorana mass terms, which correspond to coherent superpositions of particle-particle and particle-hole channels in the fermionic language. We find that attractive interactions induce three different mass terms. One is a coherent superposition of imaginary s-wave pairing and current order, and another combines a charge-density-wave and finite-momentum singlet pairing. Repulsive interactions, on the other hand, lead to ferromagnetism together with spin-triplet pairing at the edge. Our quantum Monte Carlo simulations confirm these findings and demonstrate that these instabilities occur even in the presence of strong quantum fluctuations. We discuss the implications of our results for experiments on cuprate high-temperature superconductors.
Topological superconductors, such as noncentrosymmetric superconductors with strong spin-orbit coupling, exhibit protected zero-energy surface states, which possess an intricate helical spin structure. We show that this nontrival spin character of th
e surface states can be tested experimentally from the absence of certain backscattering processes in Fourier-transform scanning tunneling measurements. A detailed theoretical analysis is given of the quasiparticle scattering interference on the surface of both nodal and fully gapped topological superconductors with different crystal point-group symmetries. We determine the universal features in the interference patterns resulting from magnetic and nonmagnetic scattering processes of the surface quasiparticles. It is shown that Fourier-transform scanning tunneling spectroscopy allows us to uniquely distinguish among different types of topological surface states, such as zero-energy flat bands, arc surface states, and helical Majorana modes, which in turn provides valuable information on the spin and orbital pairing symmetry of the bulk superconducting state.
